russ_watters said:
I wouldn't bother with drag here. While drag is a significant fraction of your engine load when cruising at 60 mph, it is an insignificant fraction of engine load when accelerating to 60mph. ...
I agree.
Here is my simplified formula (for electric cars) obtained by finding the best fit in Excel:
##t_{60}=\frac{2.79 m}{P^{0.46}T^{0.72}}##
where m is the kerb weight in Kg, P is the max power in kW and T is torque in Nm.
This is a table for performance of electric cars obtained from an earlier post with some modifications and additions:
Data for electric cars:
kg, kW, Nm, top mph, sec to 60mph*, predicted ##t_{60}##
Smart fortwo electric drive 900, 55, 130, 78, 12.9, 13.5
Mitsubishi i-MiEV 1185, 47, 180, 80, 13.5, 13.4
Citroen zEro 1185, 47, 180, 80, 13.5, 13.4
Peugeot iOn 1185, 47, 180, 81, 13.5, 13.4
Renault Zoe 1392, 65, 220, 84, 13.5*, 12.4
Renault Fluence Z.E. 1543, 70, 226, 84, 13.7*, 12.8
Nissan leaf 1595, 80, 280, 93, 9.9, 10.3
Toyota RAV4 EV 1560, 115, 296, 100, 8.0, 8.2
Tesla S 1999, 225, 430, 120, 5.9, 5.9
Tesla S Perf 2108, 270, 440, 125, 5.4, 5.6
Tesla S Perf Plus 2108, 310, 600, 130, 4.2, 4.2
The Chevrolet Volt and Toyota Prius have been removed from the table as they are hybrid cars with internal combustion engines and the Tesla models have been added to increase the range of data in the table. It should be noted that it is not always clear if the manufacturers include battery weight in their quoted kerb figures and legislation does not appear to have caught up with how the kerb weight of electric cars is defined.
* The Renault 0 to 60mph figures have been highlighted as they are actually figures for 0 to 62mph and because there is some variation on the figures quoted depending on the source. These are the sources I used: http://www.motorline.co.uk/renault/pdfs/fluence-ze.pdf and
http://www.carfolio.com/specifications/models/car/?car=342397
jumpjack said:
Just consider electric vehicles: constant torque, no gears, motor efficiency =~100% .
In a second instance we could investigate Power/Torque correlation in electric motors.
While the lack of gears for electric cars simplifies the calculations, there is still an effective gear ratio in the drive train from the motor to the wheels and this varies from model to model. This is not taken into account in my simplified formula, as this information is not readily available (but I haven't looked that hard). I am also assuming that not all electric cars are direct drive. Maybe none are? Anyone know?
Including the top speed in the calculations would help the accuracy as it gives an idea of how efficient the aerodynamics of the car are and the overall gearing of the car, but if you are going to the trouble of finding the top speed on a test track, you might as well test the 0 to 60 mph times while you are there.